===== Lecture plan =====

The curriculum is taken from A. Quarteroni (Q), [[http://www.springerlink.com/content/978-88-470-1070-3/#section=655216&page=1|Numerical Models for Differential Problems]], Springer 2008. \\
We will also use some material from Brenner & Scott (BS): [[http://www.springerlink.com/content/978-0-387-75933-3/#section=144131&page=1|The Mathematical Theory for Finite Element Methods]], Springer 2008.  

The topics included are: 

  * Introduction
  * The Poisson equation:   
    * Weak formulation
    * Finite element method
    * Implementation 
    * Error analysis 
  * Finite element function spaces
  * Abstract formalism 
  * Steady convection-diffusion problem
  * Time-dependent convection-diffusion problem.  


==== Schedule =====
**Lectures:** Monday and Tuesday. \\
Known changes are listed. \\
The topics will be described as we proceed. 

^Lecture ^Topics  ^Reading|
^19.08 | Introduction. FEM-History and FEM applications. | Slides |  
^20.08 | Poisson: PDE, Minimization and weak form.  | [[http://www.math.ntnu.no/emner/TMA4220/2013h/notes/TMA4220_2007-Lecture_Note_1.pdf|LN-1]] and Chapter 1. in Quarteroni|
^26.08 | Mathematical Background. \\   | [[http://www.math.ntnu.no/emner/TMA4220/2013h/notes/TMA4220_2007-Lecture_Note_1.pdf|LN-1]] and Chapter 2. in Quarteroni |
^27.08 | Definitions of Lebesgue and Sobolov spaces  | [[http://www.math.ntnu.no/emner/TMA4220/2013h/notes/TMA4220_2007-Lecture_Note_1.pdf|LN-1]] and Chapter 1. in Brenner & Scott|
^02.09 | Discretization of the Poisson Problem in \(R^1\) : Formulation. |[[http://www.math.ntnu.no/emner/TMA4220/2013h/notes/TMA4220_2007-Lecture_Note_2.pdf|LN-2]] and Sections 3.1 and 3.2 in Quarteroni|
^03.09 | Discretization of the Poisson problem in \(R^1\). Formulation (continue) | [[http://www.math.ntnu.no/emner/TMA4220/2013h/notes/TMA4220_2007-Lecture_Note_2.pdf|LN-2]] and Section 3.2 in Quarteroni |
^09.09 | Discretization of the Poisson Problem in \(R^1\): Theory |[[http://www.math.ntnu.no/emner/TMA4220/2013h/notes/TMA4220_2007-Lecture_Note_3.pdf|LN-3]] and Sections 4.1-4.3 in Quarteroni  |
^10.09 | Discretization of the Poisson Problem in \(R^1\): Implementation |[[http://www.math.ntnu.no/emner/TMA4220/2013h/notes/TMA4220_2007-Lecture_Note_3.pdf|LN-3]]  | \\
^16.09 | FEM for the Poisson Problem in \(R^2\)| [[http://www.math.ntnu.no/emner/TMA4220/2013h/notes/TMA4220_2007-Lecture_Note_4.pdf|LN-4]] and Section 4.4 in Quarteroni  |
^17.09 | FEM for the Poisson Problem in \(R^2\) (continnue) | [[http://www.math.ntnu.no/emner/TMA4220/2013h/notes/TMA4220_2007-Lecture_Note_4.pdf|LN-4]] and Section 4.4 in Quarteroni|
^23.09 | Abstract FEM: Construction of a Finite Element Space | Chapter 3. in Brenner & Scott  |
^24.09 | Triangular elements | Chapter 3. in Brenner & Scott  |
^30.09 | Triangular elements (continued)  | Chapter 3. in Brenner & Scott  | | \\
^01.10 | Quadrilateral Elements| Chapter 3. in Brenner and Scott  | 
^07.10 | Isoparametric mapping  | {{ :tma4220:2019h:ronquist-deformed_geometries.pdf | Deformed Geometries}}, [[http://kis.tu.kielce.pl//mo/COLORADO_FEM/colorado/IFEM.Ch16.pdf| IFEM Ch16]] and [[http://kis.tu.kielce.pl//mo/COLORADO_FEM/colorado/IFEM.Ch17.pdf| IFEM Ch17]] | \\
^08.10 | Adaptive FEM (AFEM): A priori estimates| AFEM-notes_TMA4220. Get copies at IMF-office (7th floor SB2)|\\
^14.10 | No lecture |
^15.10 | Adaptive FEM (AFEM): Adaptive refinement| AFEM-notes_TMA4220. Get copies at IMF-office (7th floor SB2)|\\
^21.10 | Spectrum of Laplace operator | {{ :tma4220:2019h:ronquist-spectra_laplace_operator.pdf | Spectrum of Laplace Operator}}| \\
^22.10 | Time-dependent diffusion | {{ :tma4220:2019h:ronquist-time_dependent_diffusion.pdf | Time-dependent diffusion }}| \\
^28.10 | Convection-Diffusion. Introduction| [[http://www.math.ntnu.no/emner/TMA4220/2013h/notes/Ronquist-Steady_Convection_Diffusion-Introduction.pdf|ER-1]] |
^29.10 | Convection-Diffusion: Theory| [[http://www.math.ntnu.no/emner/TMA4220/2013h/notes/Ronquist-Steady_Convection_Diffusion-Theory.pdf|ER-2]]  |
^04.11 | No lecture |
^05.11 | Convection-Diffusion: Example| [[http://www.math.ntnu.no/emner/TMA4220/2013h/notes/Ronquist-Steady_Convection_Diffusion-Example.pdf|ER-3]] |
^11.11 | No lecture (Project work)|  |
^12.11 | No lecture (Project work)|  |
^18.11 | No lecture (Project work)|  |
^19.11 | No lecture (Project work)|  |